Measures Of Dispersion
ICSE · Class 11 · Economics
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Quick Quiz: Measures Of Dispersion
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A continuous series has class intervals 0-10, 10-20, 20-30, 30-40, and 40-50. Using Method II, what is the range?
In the grouped data 1-10, 11-20, 21-30, and 31-40, what is the range after converting to exclusive form?
A frequency distribution has Q1 = 28 and Q3 = 52. What is the quartile deviation?
For an individual series of 7 items, the ordered values are 4, 6, 8, 10, 12, 14, and 16. What is Q1?
Sample Questions
A series has X values 5, 7, 9, 11, and 13. What is the standard deviation by actual mean method?
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2.83
Mean = 9. Deviations are -4, -2, 0, 2, 4. Squares are 16, 4, 0, 4, 16. Sum of squares = 40. SD = √(40/5) = √8 = 2.83.
Using step deviation, values 10, 20, 30, 40, 50, 60, 70 with frequencies 3, 5, 7, 9, 8, 5, 3 and A = 40, C = 10 give what standard deviation?
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16.5
Step deviation values are -3, -2, -1, 0, 1, 2, 3. Compute Σfd' = 1 and Σfd'² = 109, N = 40. SD = √[109/40 - (1/40)²] × 10 ≈ 16.5.
Two groups have the same mean 53. Group 1 has N = 40 and SD = 19. Group 2 has N = 50 and SD = 8. What is the combined standard deviation?
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14
Since both means are 53, D1 = 0 and D2 = 0. Combined SD = √[(40×19² + 50×8²) / 90] = √(17640/90) = √196 = 14.
The values 3, 6, 9, 12, and 15 have mean 9. What is the variance?
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18
Deviations from mean are -6, -3, 0, 3, 6. Squares sum to 90. Variance = average squared deviation = 90/5 = 18.
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